Lytova [1]} obtains concentration inequalities for quadratic forms in non-symmetric random tensors \(X^{(1)}\otimes \ldots \otimes X^{(d)}\)  generated by \(d\)  independent copies of an isotropic random vector \(X\)  in \({\mathbb {R}}^n\) , quadratic forms in which concentrate around their means. In the simplest \(L_2\)  case, the results of [1]} are derived from the Efron-Stein inequality for the variance of a function in \(\lbrace X^{(k)}\rbrace _{k=1}^d\) . When all \(X=X(n)\) , \(n\in {\mathbb {N}},\)  have independent entries with uniformly bounded fourth moments, Theorem 1.2 and Remark 4.1 in [1]} give a version of the MP theorem for the non-symmetric random tensor model under the assumption \(d=o(n)\)  (that seems to be optimal). Recently, Vershynin [4]} proves corresponding exponential concentration inequalities, assuming that \(X\)  has independent subgaussian entries.
